Question: Solve for $x$ : $3x^2 + 45x + 150 = 0$
Answer: Dividing both sides by $3$ gives: $ x^2 + {15}x + {50} = 0 $ The coefficient on the $x$ term is $15$ and the constant term is $50$ , so we need to find two numbers that add up to $15$ and multiply to $50$ The two numbers $5$ and $10$ satisfy both conditions: $ {5} + {10} = {15} $ $ {5} \times {10} = {50} $ $(x + {5}) (x + {10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 5) (x + 10) = 0$ $x + 5 = 0$ or $x + 10 = 0$ Thus, $x = -5$ and $x = -10$ are the solutions.